TY - JOUR

T1 - Approximation algorithms and an integer program for multi-level graph spanners

AU - Ahmed, Reyan

AU - Hamm, Keaton

AU - Jebelli, Mohammad Javad Latifi

AU - Kobourov, Stephen

AU - Sahneh, Faryad Darabi

AU - Spence, Richard

N1 - Publisher Copyright:
Copyright © 2019, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - Given a weighted graph G (V, E) and t ≥ 1, a subgraph H is a t-spanner of G if the lengths of shortest paths in G are preserved in H up to a multiplicative factor of t. The subsetwise spanner problem aims to preserve distances in G for only a subset of the vertices. We generalize the minimum-cost subsetwise spanner problem to one where vertices appear on multiple levels, which we call the multi-level graph spanner (MLGS) problem, and describe two simple heuristics. Applications of this problem include road/network building and multi-level graph visualization, especially where vertices may require different grades of service. We formulate a 0-1 integer linear program (ILP) of size O (|E|| V|2) for the more general minimum pairwise spanner problem, which resolves an open question by Sigurd and Zachariasen on whether this problem admits a useful polynomial-size ILP. We extend this ILP formulation to the MLGS problem, and evaluate the heuristic and ILP performance on random graphs of up to 100 vertices and 500 edges.

AB - Given a weighted graph G (V, E) and t ≥ 1, a subgraph H is a t-spanner of G if the lengths of shortest paths in G are preserved in H up to a multiplicative factor of t. The subsetwise spanner problem aims to preserve distances in G for only a subset of the vertices. We generalize the minimum-cost subsetwise spanner problem to one where vertices appear on multiple levels, which we call the multi-level graph spanner (MLGS) problem, and describe two simple heuristics. Applications of this problem include road/network building and multi-level graph visualization, especially where vertices may require different grades of service. We formulate a 0-1 integer linear program (ILP) of size O (|E|| V|2) for the more general minimum pairwise spanner problem, which resolves an open question by Sigurd and Zachariasen on whether this problem admits a useful polynomial-size ILP. We extend this ILP formulation to the MLGS problem, and evaluate the heuristic and ILP performance on random graphs of up to 100 vertices and 500 edges.

KW - Graph spanners

KW - Integer programming

KW - Multi-level graph representation

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M3 - Article

AN - SCOPUS:85093445182

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -